Haven't seen the movie yet but here goes:
From a real world perspective - no there is no reason a female agent wouldn't be assigned.
An agent is an agent doesn't matter male or female. There are female agents who are more or less capable and there are male agents who are more or less capable. It all depends.
From a movie / storyteller perspective female agent is more dramatic
As for a lone agent, in Indian country the FBI genrally provides investigative support with major cases for the BIA police in the same way state investigators like the Texas Rangers will support smaller LEA's in rural areas elsewhere. In many of these areas all LE is spread pretty thin.
Being a detective/ investigator is not like being a patrol officer. While the unexpected certainly happens, you are normally initiating enforcement actions not reacting. You should generally be picking the time, place and circumstances of most arrests to be most favorable to you - think of Craig Douglas and William Aprill's "unequal initiative" applied to criminals instead of by criminals.
That said it is unlikely an agent would be assigned to assist BIA with something like this unless they assigned or at least TDY to the office with jurisdiction. For all LE the smaller the office the more variety of assignments one will be required to handle.